Re: Add the numbers in a 9x9 multiplication Table

In article <1026gbt$gsd0$1@dont-email.me>,
David Entwistle  <qnivq.ragjvfgyr@ogvagrearg.pbz> wrote:

Given the sequence 0, 1, 9, 36, 100, 225, 441... it is possible to
calculate the polynomial expression for the sum of the entries in a
multiplication table of n rows and n columns. 2025 is the 9th entry in
this sequence as it is the sum for the entries in a 9 x 9 multiplication
table.
>
Can you calculate that function?

   sum(x=1..n) sum(y=1..n) [xy]
=  sum(x=1..n) [x sum(y=1..n) y]
=  [sum(x=1..n) x] [sum(y=1..n) y]
=  [sum(x=1..n)]^2

sum(x=1..n) is well known and easily seen geometrically.

-- Richard